6(2x-5)(2x+5)=11+12x+30-22x+55

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Solution for 6(2x-5)(2x+5)=11+12x+30-22x+55 equation:


Simplifying
6(2x + -5)(2x + 5) = 11 + 12x + 30 + -22x + 55

Reorder the terms:
6(-5 + 2x)(2x + 5) = 11 + 12x + 30 + -22x + 55

Reorder the terms:
6(-5 + 2x)(5 + 2x) = 11 + 12x + 30 + -22x + 55

Multiply (-5 + 2x) * (5 + 2x)
6(-5(5 + 2x) + 2x * (5 + 2x)) = 11 + 12x + 30 + -22x + 55
6((5 * -5 + 2x * -5) + 2x * (5 + 2x)) = 11 + 12x + 30 + -22x + 55
6((-25 + -10x) + 2x * (5 + 2x)) = 11 + 12x + 30 + -22x + 55
6(-25 + -10x + (5 * 2x + 2x * 2x)) = 11 + 12x + 30 + -22x + 55
6(-25 + -10x + (10x + 4x2)) = 11 + 12x + 30 + -22x + 55

Combine like terms: -10x + 10x = 0
6(-25 + 0 + 4x2) = 11 + 12x + 30 + -22x + 55
6(-25 + 4x2) = 11 + 12x + 30 + -22x + 55
(-25 * 6 + 4x2 * 6) = 11 + 12x + 30 + -22x + 55
(-150 + 24x2) = 11 + 12x + 30 + -22x + 55

Reorder the terms:
-150 + 24x2 = 11 + 30 + 55 + 12x + -22x

Combine like terms: 11 + 30 = 41
-150 + 24x2 = 41 + 55 + 12x + -22x

Combine like terms: 41 + 55 = 96
-150 + 24x2 = 96 + 12x + -22x

Combine like terms: 12x + -22x = -10x
-150 + 24x2 = 96 + -10x

Solving
-150 + 24x2 = 96 + -10x

Solving for variable 'x'.

Reorder the terms:
-150 + -96 + 10x + 24x2 = 96 + -10x + -96 + 10x

Combine like terms: -150 + -96 = -246
-246 + 10x + 24x2 = 96 + -10x + -96 + 10x

Reorder the terms:
-246 + 10x + 24x2 = 96 + -96 + -10x + 10x

Combine like terms: 96 + -96 = 0
-246 + 10x + 24x2 = 0 + -10x + 10x
-246 + 10x + 24x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-246 + 10x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-123 + 5x + 12x2) = 0

Factor a trinomial.
2((-41 + -12x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-41 + -12x)' equal to zero and attempt to solve: Simplifying -41 + -12x = 0 Solving -41 + -12x = 0 Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + -12x = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -12x = 0 + 41 -12x = 0 + 41 Combine like terms: 0 + 41 = 41 -12x = 41 Divide each side by '-12'. x = -3.416666667 Simplifying x = -3.416666667

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-3.416666667, 3}

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